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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="metric_1.html#V6" title="METRIC_1:attr.6">Reflexive</a>  <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  <a href="compl_sp.html#V1" title="COMPL_SP:attr.1">bounded</a> <a href="kurato_2.html#NM1" title="KURATO_2:NM.1">SetSequence</a> of <font color="Maroon" title="c1">M</font>;<br/>



<b>set </b><font color="Maroon" title="c3">d</font> =  <a href="compl_sp.html#K1" title="COMPL_SP:func.1">diameter</a> <font color="Maroon" title="c2">S</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><a NAME="E1:4_1"/>
( <font color="Maroon" title="c2">S</font> <a href="flang_1.html#K5" title="FLANG_1:func.5">.</a> <font color="Maroon" title="c4">n</font> is <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a> &amp;  <a href="tbsp_1.html#K2" title="TBSP_1:func.2">diameter</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">S</font> <a href="flang_1.html#K5" title="FLANG_1:func.5">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="compl_sp.html#K1" title="COMPL_SP:func.1">diameter</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">n</font> )
 <b>by </b><i><a class="ref" href="compl_sp.html#D1" target="_self" title="COMPL_SP:def.1">def1</a>, <a class="ref" href="compl_sp.html#D2" target="_self" title="COMPL_SP:def.2">def2</a></i>;<br/><a NAME="E2:4_1"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="compl_sp.html#K1" title="COMPL_SP:func.1">diameter</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="ref" href="tbsp_1.html#T29" title="TBSP_1:th.29">TBSP_1:29</a></i>;<br/><b>hence </b><a NAME="E3:4_1"/>
 <a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="compl_sp.html#K1" title="COMPL_SP:func.1">diameter</a> <font color="Maroon" title="c2">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:4"/>
 <a href="compl_sp.html#K1" title="COMPL_SP:func.1">diameter</a> <font color="Maroon" title="c2">S</font> is <a href="seq_2.html#V2" title="SEQ_2:attr.2">bounded_below</a>
 <b>by </b><i><a class="ref" href="seq_2.html#D4" title="SEQ_2:def.4">SEQ_2:def 4</a></i>;<br/>


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